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We use spectral method to prove a joint equidistribution of primitiverational points and the same along expanding horocycle orbits in the productsof the circle and the unit cotangent bundle of the modular surface. This resultexplicates the error bound in a recent work of Einsiedler, Luethi, and Shah\cite[Theorem $1.1$]{ELS}. The error is sharp upon the best known progresstowards the Ramanujan conjecture at the finite places for the modular surface.

Joint equidistribution on the product of the circle and the unit tangent bundle of the modular surface